Rewrite as a simplified fraction. ${0.6\overline{91} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 691.9191...\\ 10x &= 6.9191...\end{align*}}$ Subtracting the two equations, we have: ${990x = 685}$ ${x = \dfrac{685}{990}} $ ${x = \dfrac{137}{198}} $